Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
NDA 2021
Exam
NDA
Year
2021
Subject
Mathematics
Chapter
Application of Derivatives

NDA 2021 · Mathematics · Application of Derivatives

What is the condition that f(x)=x^3+x^2+k x has no local extremum?

What is the condition that f(x)=x3+x2+kxf(x)=x^3+x^2+k x has no local extremum?

Options

  1. A4k<14 k < 1
  2. B3k>13 k > 1
  3. C3k<13 k < 1
  4. D3k≤13 k \leq 1

Correct answer

B. 3k>13 k > 1

Step-by-step solution

f(x)=x3+x2+kxf′(x)=3x2+2x+k\begin{aligned} & f(x)=x^3+x^2+k x \\ & f^{\prime}(x)=3 x^2+2 x+k \end{aligned} For no local extremum D<0D < 0⇒(2)2−4(3)(k)<0⇒4×3×k>0⇒3k>1.\begin{aligned} & \Rightarrow(2)^2-4(3)(k) < 0 \\ & \Rightarrow 4 \times 3 \times k > 0 \\ & \Rightarrow 3 k > 1. \end{aligned}$$
Practice Application of Derivatives on Quantrex Academy →

More from Application of Derivatives

Passage: Let S and T be the sets where f(x)=(x^3)/(3)-(5x^2)/(2)+6x+7 decreases and… NDA 2026What is the length of the longest interval in which the function f(x)=2 ^2 x-1 is… NDA 2026Passage: Let S and T be the sets where f(x)=(x^3)/(3)-(5x^2)/(2)+6x+7 decreases and… NDA 2026For the following three (03) items: Let y = f(x) = x ^ -1 x 1 - x^2 + 1 - x^2 . What is… NDA 2025Consider the following statements regarding the function f(x) = (1)/(x - 5)… NDA 2025Consider the following for the two (02) items that follow: Let ABC be a triangle… NDA 2025Consider the following for the two (02) items that follow: Let ABC be a triangle… NDA 2025A wire of length 20 cm is to be bent into a rectangle. Which of the following statements… NDA 2025Consider the following for the two (02) items that follow: Let the function f(x) = x^2 +… NDA 2025For the following two (02) items: Consider the function f(x) = 1 - [3] (x-1)^2 . The… NDA 2025Consider the following for the two (02) items that follow: The slope of the tangent to… NDA 2025For the following three (03) items: Consider the function f(x) = x|x| . Consider the… NDA 2025Consider the following statements: Statement-I: The function f(x) = (x^3 + 128)/(x) has a… NDA 2025Paragraph: Let f(x)= 2 x+x on [(-π)/(2), (π)/(2)] Question: What is the greatest value of… NDA 2024Let f(x)=(x)/( x) ;(x > 1) Consider the following statements: 1. f(x) is increasing in… NDA 2024Paragraph: Let f(x)= 2 x+x on [(-π)/(2), (π)/(2)] Question: What is the least value of… NDA 2024 Full Application of Derivatives list Application of Derivatives JEE Maths PYQsJEE Mathematics PYQs All NDA PYQs